Consistent Tests for Conditional Treatment Effects

We construct a Kolmogorov-Smirnov test for the null hypothesis that the conditional average treatment effect is non-negative conditional on every possible value of the covariates. The null hypothesis can be characterized as a conditional moment inequality under the unconfoundedness assumption, and we employ the instrumental variable method in Andrews and Shi (2013) to convert the conditional moment inequality into an infinite number of unconditional moment inequalities without information loss. A Kolmogorov- Smirnov test is constructed based on these unconditional moment inequalities. It is shown that our test can control the size uniformly over a broad set of data generating processes asymptotically, is consistent against fixed alternatives and is unbiased against some N−1/2 local alternatives. We also consider several extensions of our test.